A non-local two-phase flow model for immiscible displacement in highly heterogeneous porous media and its parametrization
A non-local two-phase flow model for immiscible displacement in highly heterogeneous porous media and its parametrization
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DOI：
10.1016/j.advwatres.2013.05.012
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发表时间：
2013-12
影响因子：
4.7
通讯作者：
J. Tecklenburg;I. Neuweiler;M. Dentz;J. Carrera;S. Geiger;Christian Abramowski;O. Silva
中科院分区：
文献类型：
--
作者：
J. Tecklenburg;I. Neuweiler;M. Dentz;J. Carrera;S. Geiger;Christian Abramowski;O. Silva
在本文中，我们提出了高度非均质介质中水平非混相位移的一个升级模型。例如，这种非均质性可以在裂缝性岩石中发现，裂缝性岩石由两个流动域组成，一个是可移动的裂缝，一个是几乎不移动的基质。我们利用均质化理论推导了一种能够预测移动-不移动区域流动的升级双连续介质模型。该模型由裂缝域中驱替流体饱和度流动方程和基质中毛细管饱和度流动方程组成，两者通过源项耦合。通过在矩阵域中线性化毛细管逆流，我们将该方程组合并为裂缝饱和度的非局部单方程模型，该模型可以解释为非混相位移的多速率传质（MRMT）模型。我们讨论了这种简化，并根据从岩石样品中获得的局部水力参数和从裂缝网络的平均流动特性的知识来参数化升级模型方程。我们通过考虑一条具有渗吸的裂缝进入矩形矩阵域，证明了它在预测两相流方面的性能。升级模型直接从参考模型的几何参数、基质水力参数和裂缝参数进行参数化，不需要进行参数拟合。我们比较了详细模型和放大模型在介质控制平面上驱替流体的突破曲线。详细的数值模拟和放大后的模型都显示出逆电流填充矩阵的前渐近t-1/2尺度和特征时间尺度上的中断。
In this paper, we present an upscaled model for horizontal immiscible displacement in highly heterogeneous media. This type of heterogeneity can be found, for instance, in fractured rock, which consists of two flow domains, a mobile fracture and a virtually immobile matrix. We derive an upscaled double-continuum model capable of predicting flow in mobile–immobile domains using homogenization theory. The model consists of a flow equation for the saturation of displacing fluid in the fracture domain, and a capillary flow equation for saturation in the matrix, which are coupled via a source term. By linearizing capillary counter current flow in the matrix domain, we combine this system of equations into a non-local single-equation model for the fracture saturation, which can be interpreted as a multi-rate mass-transfer (MRMT) model for immiscible displacement. We discuss this simplification and the parametrization of the upscaled model equation from local hydraulic parameters obtained from rock samples and from knowledge of the average flow properties of the fracture network. We demonstrate its performance for predicting two-phase flow by considering a single fracture with imbibition into a rectangular matrix domain. The upscaled model is parameterized directly from geometry and hydraulic parameters of matrix and fracture of the reference model, which means that no parameters need to be fitted. We compare the detailed and upscaled models in terms of breakthrough curves for the displaced fluid at a control plane within the medium. Both the detailed numerical simulations and the upscaled model show a preasymptotic t-1/2 scaling and a breakoff at the characteristic time scale for filling the matrix by counter current flow.